Your weekly cost (in dollars) to manufacture x cars and y trucks is given by $C ( x , y ) = 300,000 + 6,500 x + 4,500 y$
Find $\frac { \partial C } { \partial x }$ , and $\frac { \partial C } { \partial y }$ .

A) $\frac { \partial C } { \partial x } = 4,500$ , $\frac { \partial C } { \partial y } = 6,500$
B) $\frac { \partial C } { \partial x } = 11,000$ , $\frac { \partial C } { \partial y } = 2,000$
C) $\frac { \partial C } { \partial x } = 300,000$ , $\frac { \partial C } { \partial y } = 300,000$
D) $\frac { \partial C } { \partial x } = 6,500$ , $\frac { \partial C } { \partial y } = 4,500$
E) $\frac { \partial C } { \partial x } = - 6,500$ , $\frac { \partial C } { \partial y } = - 4,500$

Question

Your weekly cost (in dollars) to manufacture x cars and y trucks is given by   $C ( x , y ) = 300,000 + 6,500 x + 4,500 y$  
Find $\frac { \partial C } { \partial x }$ , and $\frac { \partial C } { \partial y }$ .
 
A) $\frac { \partial C } { \partial x } = 4,500$ , $\frac { \partial C } { \partial y } = 6,500$
B) $\frac { \partial C } { \partial x } = 11,000$ , $\frac { \partial C } { \partial y } = 2,000$
C) $\frac { \partial C } { \partial x } = 300,000$ , $\frac { \partial C } { \partial y } = 300,000$
D) $\frac { \partial C } { \partial x } = 6,500$ , $\frac { \partial C } { \partial y } = 4,500$
E) $\frac { \partial C } { \partial x } = - 6,500$ , $\frac { \partial C } { \partial y } = - 4,500$

Quizplus · Accepted Answer

$\frac { \partial C } { \partial x }$ represents the partial derivative of the cost function with respect to x, which is 6,500, and $\frac { \partial C } { \partial y }$ represents the partial derivative with respect to y, which is 4,500. This means for each additional car manufactured, the cost increases by $6,500, and for each additional truck, the cost increases by $4,500.

Your Weekly Cost (In Dollars) to Manufacture X Cars and Y